## [1] 16
dir01 <- here("s01")  # agreggate data (no spatial diferences)
dir1 <- here("s1")  # Data strata flishery
dir2 <- here("s2")  # Same 9 with areas (SubStrata) as fleet. Dif size comoposition and dif CPUE and dif survey length and biomass data by strata
dir3 <- here("s3")  # whitout S-R
dir4 <- here("s4")  # 
dir5 <- here("s5")  # 
dir6 <- here("s6")  # 
dir7 <- here("s7")  # 2 set parametres EMM-2024/23 (Mardones)
dirtest <- here("test")
Figs <- here("Figs")  # S

OVERVIEW

In a simple way, the core of Stock Synthesis is its population dynamics model, which represents the dynamics of krill populations over time. This model incorporates key biological, environmental and predator data sources. The model is typically formulated using mathematical equations that describe how these parameters interact to determine the abundance and distribution of krill in the study area.

Statistical model (SS3)

Stock Synthesis v.3.30.21 is a widely used software tool for assessing fish and invertebrate populations, including krill (Euphausia superba) in the Antarctic Peninsula region. The methodology employed by Stock Synthesis involves a comprehensive and integrated approach, utilizing various data sources and modeling techniques to estimate the main population variables of krill in WAP.

The stock assesment model was configured using Stock Synthesis (SS3 hereafter)SS3 (Richard Donald Methot et al., 2020; Richard D. Methot & Wetzel, 2013) with the most updated version (V.3.30.21). SS3 is a structured age and size stock evaluation model, in the class of models called “Integrated stock evaluation analysis model”. SS3 has a stock population sub-model that simulates growth, maturity, fecundity, recruitment, movement, and mortality processes, and observation sub-models and expected values for different types of data. The model is coded in C++ with estimation parameters enabled by automatic differentiation (ADMB) (Fournier et al., 2012; Richard D. Methot & Wetzel, 2013). The analysis of results and outputs uses R tools and the graphical interface of the r4ss and ss3diags library (Taylor, 2019; Winker et al., 2024).

By integrating data from multiple sources and considering spatial heterogeneity, the assessment methodology using Stock Synthesis v.3.30.21 provides a robust framework for evaluating the status of krill populations in the Antarctic Peninsula region. This information is essential for supporting management decisions aimed at ensuring the sustainable use of krill resources in this ecologically sensitive area.

Parametres

read files

Input parameters for the initial SS3 model of krill. Each parameter line contains a minimum value (LO), maximum value (HI), and initial value (INIT). If the phase (PHASE) for the parameter is negative, the parameter is fixed as input
LO HI INIT PHASE
Mortalidad natural
Nat M 0.20 0.50 0.400000 3
Crecimiento
Lmin 0.00 3.00 1.000000 2
Lmax 1.00 10.00 7.000000 4
VonBert K 0.05 0.80 0.450000 4
CV young 0.05 0.25 0.050000 -3
CV old 0.05 0.25 0.050000 -3
Relación longitud-peso
Wt a 0.00 3.00 0.000005 -3
Wt b 1.00 4.00 3.346940 -3
Ojiva de madurez
L50% 0.20 5.00 2.400000 4
Mat slope -3.00 3.00 -0.250000 4
Relación stock-recluta
SR_LN(R0) 3.00 30.00 10.000000 1
SR_BH_steep 0.20 1.00 0.750000 -4
SR_sigmaR 0.00 2.00 0.600000 -4
SR_regime -5.00 5.00 0.000000 -4
SR_autocorr 0.00 0.00 0.000000 -99
Capturabilidad
LnQ_base_FISHERYBS(1) -25.00 25.00 -3.722310 1
Q_extraSD_FISHERYBS(1) 0.00 1.00 0.000000 3
Selectividad
SizeSel_P_1_FISHERYBS(1) 0.01 8.00 2.500000 3
SizeSel_P_2_FISHERYBS(1) 1.50 8.00 2.000000 2
SizeSel_P_1_FISHERYEI(2) 0.01 8.00 2.500000 3
SizeSel_P_2_FISHERYEI(2) 1.50 8.00 2.000000 2
SizeSel_P_1_FISHERYGS(3) 0.01 8.00 2.500000 3
SizeSel_P_2_FISHERYGS(3) 1.50 8.00 2.000000 2
SizeSel_P_1_FISHERYJOIN(4) 0.01 8.00 2.500000 3
SizeSel_P_2_FISHERYJOIN(4) 1.50 8.00 2.000000 2
SizeSel_P_1_FISHERYSSIW(5) 0.01 8.00 2.500000 3
SizeSel_P_2_FISHERYSSIW(5) 1.50 8.00 2.000000 2
SizeSel_P_1_SURVEYBS(6) 1.00 7.00 2.000000 2
SizeSel_P_2_SURVEYBS(6) 1.00 7.00 1.000000 3
SizeSel_P_1_SURVEYEI(7) 1.00 7.00 2.000000 2
SizeSel_P_2_SURVEYEI(7) 1.00 7.00 1.000000 3
SizeSel_P_1_SURVEYGS(8) 1.00 7.00 2.000000 2
SizeSel_P_2_SURVEYGS(8) 1.00 7.00 1.000000 3
SizeSel_P_1_SURVEYJOIN(9) 1.00 7.00 2.000000 2
SizeSel_P_2_SURVEYJOIN(9) 1.00 7.00 1.000000 3
SizeSel_P_1_SURVEYSSIW(10) 1.00 7.00 2.000000 2
SizeSel_P_2_SURVEYSSIW(10) 1.00 7.00 1.000000 3
SizeSel_P_1_PREDATOR(11) 0.00 7.00 0.500000 -2
SizeSel_P_2_PREDATOR(11) 1.00 7.00 3.500000 -3

Scenarios

In Table 1 we have ten scenarios to test different option in modeling about main consideration in assessment of krill population.

Scenario Description
s01 Fishery and Survey (AMLR) data, Predator, Environmental aggregate data in 48.1
s1 Fishery and Survey (AMLR) data Length, Index, Catch by strata. Predator and Env data
s2 “s1” without S-R relation
s3 “s1” BH S-R relation weak (0.9 steepness)
s4 “s1” BH S-R relation strong (0.6 steepness)
s5 “s1” BH S-R relation mid-strong estimated
s6 “s1” Ricker S-R relation estimated
s7 “s1” w/ set of parameters estimated in (EMM-204/32?)

Run Models

Read outputs

RESULTS

Main Variables poulation

Total biomass

Data used en both (spatial and No spatial models)

Respecto a los valores y parametros biologicos modelados, los siguientes graficos identifican los estimadores puntuales del recurso

Diagnosis Base Model

Step to do a good practice in model diagnosis is;

  • 1.  Convergence. Final convergence criteria is 1.0e-04
  • 2.  Residual (visual and metrics)
  • 3.  Retrospective analysis (Mhon Parameter)
    1. Likelihood profile

all this framework try to follow recommendations of Carvalho et al. (2021)

Residual consistency

## 
##  Running Runs Test Diagnosics for Mean length 
## Plotting Residual Runs Tests

## 
## Runs Test stats by Mean length:
##          Index runs.p     test  sigma3.lo sigma3.hi type
## 1    FISHERYBS  0.500   Passed -0.1816665 0.1816665  len
## 2    FISHERYEI  0.145   Passed -0.2319052 0.2319052  len
## 3    FISHERYGS  0.338   Passed -0.1813395 0.1813395  len
## 4  FISHERYJOIN     NA Excluded         NA        NA  len
## 5  FISHERYSSIW  0.406   Passed -0.1476043 0.1476043  len
## 6     SURVEYBS  0.189   Passed -0.2452391 0.2452391  len
## 7     SURVEYEI  0.148   Passed -0.2482065 0.2482065  len
## 8     SURVEYGS  0.334   Passed -0.3723597 0.3723597  len
## 9   SURVEYJOIN  0.500   Passed -0.5749614 0.5749614  len
## 10    PREDATOR  0.599   Passed -0.3154527 0.3154527  len
## 
##  Running Runs Test Diagnosics for Index 
## Plotting Residual Runs Tests

## 
## Runs Test stats by Index:
##          Index runs.p     test  sigma3.lo sigma3.hi type
## 1    FISHERYBS  0.010   Failed -0.8521502 0.8521502 cpue
## 2    FISHERYEI  0.179   Passed -1.1048793 1.1048793 cpue
## 3    FISHERYGS  0.018   Failed -1.9450662 1.9450662 cpue
## 4  FISHERYJOIN  0.819   Passed -1.9136749 1.9136749 cpue
## 5  FISHERYSSIW  0.025   Failed -0.5893076 0.5893076 cpue
## 6     SURVEYBS  0.278   Passed -2.8964975 2.8964975 cpue
## 7     SURVEYEI  0.708   Passed -2.5384240 2.5384240 cpue
## 8     SURVEYGS  0.753   Passed -3.2473271 3.2473271 cpue
## 9   SURVEYJOIN  0.268   Passed -2.6879583 2.6879583 cpue
## 10  SURVEYSSIW     NA Excluded         NA        NA cpue
## 11    PREDATOR  0.002   Failed -0.7168626 0.7168626 cpue
## Plotting JABBA residual plot

## 
## RMSE stats by Index:
##    indices RMSE.perc nobs
## 1  FISHERY      44.7   21
## 2  SURVEY1      82.6   24
## 3 PREDATOR      25.8   41
## 4 Combined      52.1   86
## Plotting JABBA residual plot

## 
## RMSE stats by Index:
##        indices RMSE.perc nobs
## 1    FISHERYBS      54.3   18
## 2    FISHERYEI      40.7   20
## 3    FISHERYGS      72.8   14
## 4  FISHERYJOIN      65.6    6
## 5  FISHERYSSIW      33.8   21
## 6     SURVEYBS     102.9   21
## 7     SURVEYEI      80.5   18
## 8     SURVEYGS     111.5   20
## 9   SURVEYJOIN     108.4    8
## 10  SURVEYSSIW      52.6    2
## 11    PREDATOR      39.4   41
## 12    Combined      71.3  189
## Plotting JABBA residual plot

## 
## RMSE stats by Index:
##        indices RMSE.perc nobs
## 1    FISHERYBS      54.2   18
## 2    FISHERYEI      40.8   20
## 3    FISHERYGS      72.5   14
## 4  FISHERYJOIN      66.2    6
## 5  FISHERYSSIW      33.8   21
## 6     SURVEYBS     102.5   21
## 7     SURVEYEI      80.3   18
## 8     SURVEYGS     111.5   20
## 9   SURVEYJOIN     108.1    8
## 10  SURVEYSSIW      53.3    2
## 11    PREDATOR      39.4   41
## 12    Combined      71.2  189
## Plotting JABBA residual plot

## 
## RMSE stats by Index:
##        indices RMSE.perc nobs
## 1    FISHERYBS      54.2   18
## 2    FISHERYEI      40.8   20
## 3    FISHERYGS      72.5   14
## 4  FISHERYJOIN      66.2    6
## 5  FISHERYSSIW      33.8   21
## 6     SURVEYBS     102.5   21
## 7     SURVEYEI      80.3   18
## 8     SURVEYGS     111.5   20
## 9   SURVEYJOIN     108.1    8
## 10  SURVEYSSIW      53.3    2
## 11    PREDATOR      39.4   41
## 12    Combined      71.2  189
## Plotting JABBA residual plot

## 
## RMSE stats by Index:
##        indices RMSE.perc nobs
## 1    FISHERYBS      57.3   18
## 2    FISHERYEI      39.9   20
## 3    FISHERYGS      79.3   14
## 4  FISHERYJOIN      50.7    6
## 5  FISHERYSSIW      35.4   21
## 6     SURVEYBS     111.9   21
## 7     SURVEYEI      87.7   18
## 8     SURVEYGS     115.8   20
## 9   SURVEYJOIN     114.3    8
## 10  SURVEYSSIW      37.5    2
## 11    PREDATOR      39.4   41
## 12    Combined      74.9  189
## Plotting JABBA residual plot

## 
## RMSE stats by Index:
##        indices RMSE.perc nobs
## 1    FISHERYBS      71.4   18
## 2    FISHERYEI      46.5   20
## 3    FISHERYGS      98.4   14
## 4  FISHERYJOIN      39.6    6
## 5  FISHERYSSIW      48.0   21
## 6     SURVEYBS     118.7   20
## 7     SURVEYEI     101.1   18
## 8     SURVEYGS     110.3   19
## 9   SURVEYJOIN     136.3    8
## 10  SURVEYSSIW      14.5    2
## 11    PREDATOR      29.9   41
## 12    Combined      80.5  187
## Plotting JABBA residual plot

## 
## RMSE stats by Index:
##        indices RMSE.perc nobs
## 1    FISHERYBS      72.5   18
## 2    FISHERYEI      47.9   20
## 3    FISHERYGS     100.2   14
## 4  FISHERYJOIN      37.4    6
## 5  FISHERYSSIW      49.1   21
## 6     SURVEYBS     120.8   20
## 7     SURVEYEI     105.1   18
## 8     SURVEYGS     112.5   19
## 9   SURVEYJOIN     138.8    8
## 10  SURVEYSSIW      19.6    2
## 11    PREDATOR      39.4   41
## 12    Combined      83.1  187
## Plotting JABBA residual plot

## 
## RMSE stats by Index:
##        indices RMSE.perc nobs
## 1    FISHERYBS      56.2   18
## 2    FISHERYEI      40.0   20
## 3    FISHERYGS      77.3   14
## 4  FISHERYJOIN      53.6    6
## 5  FISHERYSSIW      34.7   21
## 6     SURVEYBS     109.2   21
## 7     SURVEYEI      86.5   18
## 8     SURVEYGS     115.0   20
## 9   SURVEYJOIN     112.2    8
## 10  SURVEYSSIW      42.7    2
## 11    PREDATOR      39.4   41
## 12    Combined      73.9  189

Relationship Stock-Recruit

Retrospective analysis

Los análisis retrospectivo, dan cuenta de diferencias de estimación (sub - sobreestimación) en los patrones entre modelos evaluados.

Hindcast Cross-Validation and prediction skill

Implementing the Hindcast Cross-Validation (HCxval) diagnostic in Stock Synthesis requires the same model outputs generated by r4ss:SS_doRetro(). As a robust measure of prediction skill, we implemented the mean absolute scaled error (MASE). In brief, the MASE score scales the mean absolute. Regarding (A MASE score > 1 indicates that the average model forecasts are worse than a random walk. Conversely, a MASE score of 0.5 indicates that the model forecasts twice as accurately as a naïve baseline prediction; thus, the model has prediction skill.

Kobe (status)

## 
##  starter.sso with Bratio: SSB/SSB0 and F: _abs_F 
## 

another

Likelihood

Convergence criteria

0.0001 final convergence criteria (e.g. 1.0e-04)

Outputs Model Base

Main variables outputs from stock asssessment krill in WAP
Yr Era Seas Bio_all Bio_smry SpawnBio Recruit_0
1679 1976 VIRG 1 3244530 3235450 1144730 1319640000
1680 1977 INIT 1 3244530 3235450 1144730 1319640000
1681 1978 TIME 1 3249980 3235450 1144730 2112190000
1682 1979 TIME 1 3307530 3287650 1144730 2890610000
1683 1980 TIME 1 3450930 3441500 1144340 1371580000
1684 1981 TIME 1 3428230 3424240 1083240 580747000
1685 1982 TIME 1 3449600 3447050 1075260 371065000
1686 1983 TIME 1 3179940 3176410 1019690 512862000
1687 1984 TIME 1 2974100 2963260 1027460 1575930000
1688 1985 TIME 1 2862610 2858110 1096720 654349000
1689 1986 TIME 1 2678740 2674570 1121100 606217000
1690 1987 TIME 1 2338860 2331870 957885 1017320000
1691 1988 TIME 1 2224460 2214040 851661 1514860000
1692 1989 TIME 1 2115770 2098060 739424 2574280000
1693 1990 TIME 1 2160480 2149170 676793 1645000000
1694 1991 TIME 1 2175200 2170750 638855 647486000
1695 1992 TIME 1 2180870 2178150 574259 395134000
1696 1993 TIME 1 2168580 2161130 560105 1082420000
1697 1994 TIME 1 2244840 2233240 632549 1686260000
1698 1995 TIME 1 2339890 2329540 738052 1505020000
1699 1996 TIME 1 2448890 2442610 860906 913517000
1700 1997 TIME 1 2521570 2517950 883197 526178000
1701 1998 TIME 1 2508190 2504250 832332 573318000
1702 1999 TIME 1 2462280 2447050 799843 2213040000
1703 2000 TIME 1 2520000 2504520 846772 2250720000
1704 2001 TIME 1 2668140 2653410 916344 2141880000
1705 2002 TIME 1 2855370 2850270 935110 741167000
1706 2003 TIME 1 2985590 2978960 902888 965164000
1707 2004 TIME 1 3057050 3049840 879122 1048360000
1708 2005 TIME 1 3101830 3085190 914406 2418740000
1709 2006 TIME 1 3259220 3244510 1084860 2138280000
1710 2007 TIME 1 3330550 3322930 1158320 1108000000
1711 2008 TIME 1 3435280 3423810 1197020 1666820000
1712 2009 TIME 1 3479050 3460490 1124160 2698050000
1713 2010 TIME 1 3589180 3569310 1104040 2888260000
1714 2011 TIME 1 3672680 3654360 1083760 2663620000
1715 2012 TIME 1 3988290 3982610 1205830 825836000
1716 2013 TIME 1 4136720 4127180 1254410 1386190000
1717 2014 TIME 1 4060520 4046150 1210280 2089470000
1718 2015 TIME 1 4025220 4013810 1254770 1659130000
1719 2016 TIME 1 3967690 3960880 1346260 989842000
1720 2017 TIME 1 3863280 3855110 1396420 1188290000
1721 2018 TIME 1 3689970 3682420 1373480 1098610000
1722 2019 TIME 1 3507920 3502770 1265680 748826000
1723 2020 TIME 1 3346120 3343480 1234730 384541000
1724 2021 FORE 1 3177260 3168120 1247410 1328760000
1725 2022 FORE 1 2968650 2959540 1193720 1324170000
1726 2023 FORE 1 2782530 2773490 1093730 1314540000
1727 2024 FORE 1 2674910 2665920 1020370 1306380000
1728 2025 FORE 1 2613310 2604390 944772 1296770000
NA NA NA NA NA NA NA NA
NA.1 NA NA NA NA NA NA NA
NA.2 NA NA NA NA NA NA NA

Comparision outputs betwwen scenarios

comparision between select models No spatialand Spatial implicit and Spatial W/ new set parametres

comparision between select models Old Paramters and New Parameters WG SAM 2024/23

Comparsion in sd long term time series

Autocorrelation in Recruit and Biomas

Recruit deviation

REFERENCES

Carvalho, F., Winker, H., Courtney, D., Kapur, M., Kell, L., Cardinale, M., Schirripa, M., Kitakado, T., Yemane, D., Piner, K. R., Maunder, M. N., Taylor, I., Wetzel, C. R., Doering, K., Johnson, K. F., & Methot, R. D. (2021). A cookbook for using model diagnostics in integrated stock assessments. Fisheries Research, 240(April), 105959. https://doi.org/10.1016/j.fishres.2021.105959
Fournier, D. A., Skaug, H. J., Ancheta, J., Ianelli, J., Magnusson, A., Maunder, M. N., Nielsen, A., & Sibert, J. (2012). AD Model Builder: Using automatic differentiation for statistical inference of highly parameterized complex nonlinear models. Optimization Methods and Software, 27(2), 233–249. https://doi.org/10.1080/10556788.2011.597854
Methot, Richard D., & Wetzel, C. R. (2013). Stock synthesis: A biological and statistical framework for fish stock assessment and fishery management. Fisheries Research, 142, 86–99. https://doi.org/10.1016/j.fishres.2012.10.012
Methot, Richard Donald, Wetzel, C. R., Taylor, I. G., & Doering, K. L. (2020). Stock synthesis user manual: Version 3.30.21 [NOAA Processed Report Series NMFS-NWFSC-PR-2020-05]. U.S. Department of Commerce. https://doi.org/10.25923/5wpn-qt71
Taylor, I. (2019). Using R for Stock Synthesis Installing R and getting R4SS. Fisheries Science, November.
Winker, H., Carvalho, F., Cardinale, M., & Kell, L. (2024). ss3diags: What the package does (one line, title case). https://github.com/jabbamodel/ss3diags